Sequence and series
Sequence and series is one of the basic topics in Arithmetic. An itemized collection of elements in which repetitions of any sort are allowed is known as a sequence, whereas series…
Laplace equation
The scalar form of Laplace's equation is the partial differential equation (1) where is the Laplacian. Note that the operator is commonly written as by mathematicians (Krantz 1999, p. 16). Laplace's equation is a special case…
Euler-Cauchy Equations
An Euler-Cauchy equation is where b and c are constant numbers. Let us consider the change of variable x = et. Then we have The equation (EC) reduces to the new equation We recognize a second…
Numerical Methods: The Trapezium Rule and Simpson’s Rule
Integrals don't have to get very complicated before symbolic methods fail to work. Consider, for example, the integral 01cos(x3+x)dx: there are no know symbolic methods, based on indefinite integration, that…
Correlation and regression
The word correlation is used in everyday life to denote some form of association. We might say that we have noticed a correlation between foggy days and attacks of wheeziness.…
Discrete and Continuous Random Variables
A variable is a quantity whose value changes. A discrete variable is a variable whose value is obtained by counting. Examples: number of students present number of red marbles in a jar number…
Bayes’ Theorem
Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. Subjectivists, who maintain that rational belief is governed…
Conditional Probability
The conditional probability of an event B is the probability that the event will occur given the knowledge that an event A has already occurred. This probability is written P(B|A), notation for the probability of B given A.…
Axioms of probability
Chance is a slippery concept. We all know that some random events are more likely to occur than others, but how do you quantify such differences? How do you work…
Half Range Fourier Series
If a function is defined over half the range, say , instead of the full range from , it may be expanded in a series of sine terms only or of cosine…
